Displaying similar documents to “Absolute stable rank and Witt cancellation for noncommutative rings.”

On the unit-1-stable rank of rings of analytic functions.

Joan Josep Carmona, Julià Cufí, Pere Menal (1992)

Publicacions Matemàtiques

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In this paper we prove a general result for the ring H(U) of the analytic functions on an open set U in the complex plane which implies that H(U) has not unit-1-stable rank and that has some other interesting consequences. We prove also that in H(U) there are no totally reducible elements different from the zero function.

Constructing ω-stable structures: Computing rank

John T. Baldwin, Kitty Holland (2001)

Fundamenta Mathematicae

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This is a sequel to [1]. Here we give careful attention to the difficulties of calculating Morley and U-rank of the infinite rank ω-stable theories constructed by variants of Hrushovski's methods. Sample result: For every k < ω, there is an ω-stable expansion of any algebraically closed field which has Morley rank ω × k. We include a corrected proof of the lemma in [1] establishing that the generic model is ω-saturated in the rank 2 case.